Skip to main content


Dual condensate of fermions and excitons should exist, say theoretical chemists

09 Mar 2020
Condensate collaborators
Condensate collaborators: left to right are Shiva Safaei, David Mazziotti, and LeeAnn Sager. (Courtesy: Eddie Quinones/University of Chicago)

It should be possible to create materials that conduct both electric current and exciton excitation energy with 100% efficiency and at relatively high temperatures – according to theoretical chemists in the US. They have calculated that such materials would exist in a single quantum state but would demonstrate properties of two different condensates – one made from excitons and the other made from pairs of fermions.

Bose–Einstein condensates are made by cooling a gas of particles sufficiently that the de Broglie wavelengths of individual particles are comparable to the spacing between particles – allowing the system to condense into a single quantum ground state. The particles must be bosons, which have integer spin and can therefore all occupy the same quantum state simultaneously. However, condensates can also be made from bound-pairs of half-integer-spin fermions because pairs of fermions have integer spin and are therefore bosons.

In a superconductor, bound pairs of electrons (fermions) create a superfluid that allows electrical current to flow through the material without resistance. These “Cooper pairs” have a low binding energy, which means they are easily destroyed by thermal energy. Above a relatively low critical temperature, the pairs break apart and the material becomes a normal conductor.

Excited electrons

One possible way to boost the critical temperature of a condensate is to make it from excitons (bosons), which are electrons bound to holes. An exciton is created when an electron is excited from the valence band of a material – leaving behind the hole. A condensate of excitons can therefore carry this excitation energy through a material without resistance. Unlike Cooper pairs, however, excitons do not carry electrical charge. Excitons are more tightly bound than Cooper pairs, meaning that such condensates could persist at higher temperatures than superconductors. However, because particles and holes naturally annihilate very quickly, exciton condensates are hard to make.

Exciton condensates can be generated by placing the electrons in an optical trap or using twin layers of material such as semiconductor or graphene to keep particles and holes apart. Exciton condensates can also co-exist alongside fermion-pair condensates, where they allow Cooper pairs to exist at higher temperatures. Two years ago, for example, physicists at Royal Holloway, University of London, and the University of Southampton in the UK combined a superconducting ring with a semiconductor microcavity.

This latest research was done by LeeAnn Sager, Shiva Safaei and David Mazziotti at the University of Chicago. Mazziotti points out that the properties of the two types of condensate remain distinct from one another in such systems. The trio investigated whether it is theoretically possible to create a material that displays both sets of properties together. Such a material, they say, might be able to conduct both electricity and excitation energy with complete efficiency.

“Large family of wave functions”

The researchers first used a computer model to simulate the behaviour of a four-particle fermionic system, finding that it would indeed exhibit these dual properties. Lacking the processing power to scale this system up, they then calculated what would happen when entangling the quantum wave functions of a superconductor and an exciton condensate containing large numbers of particles. Doing so, says Mazziotti, they showed that there should be “a pretty large family of wave functions that combine these properties and in principle exist in the macroscopic world”.

Reporting their results in Physical Review B, the researchers say that this single quantum state, which they call a “fermion-exciton condensate”, combines the properties of the individual condensates “in a highly nontrivial manner”. They explain that the properties of each condensate are reduced somewhat when compared to their creation in isolation. However, this compromise diminishes as the number of electrons in the system goes up.

Mazziotti says that the group is now working with experimentalists to create such a material in the lab. Rather than using two semiconductor layers to create a purely excitonic condensate, he says that the most obvious candidate for a fermion-exciton condensate would be a pair of superconducting layers – although at this stage he does not know what type of superconductor they would use. “This would be the shake-and-bake recipe for materials that have these dual properties,” he quips.

However, Mazziotti is under no illusion that this is an easy project. One challenge, he says, will be handling the different binding energies of the Cooper pairs and excitons. Sager adds that it will be tricky to bring the layers close enough to create the bound pairs but not so close that electrons can tunnel from one layer to the other. But if those hurdles can be overcome then applications beckon, says Mazziotti. One possible use, he suggests, might be in medical imaging – with propagation of visible light without loss preserving resolution.

Peter Abbamonte of the University of Illinois, who was not involved in the research, feels “some luck would certainly be needed” to realise such a condensate in the lab. But he reckons that the theoretical result “makes a compelling case” for trying to construct exciton condensate-like structures from superconducting constituents.

Copyright © 2022 by IOP Publishing Ltd and individual contributors
bright-rec iop pub iop-science physcis connect